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C7×D48 #10620597

order672
isoclinismisoclinic class of D48
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D48

Splittings

FittingC3×C7×C16 ⋊ C2
HallC3×C7 ⋊ D16
SylowC3 ⋊ C7×D16

Subgroups

subgroupG/H
centerC2×C7D24
commutator, cosocleC3×C8C22×C7
FrattiniC8C2×D3×C7
FittingC3×C7×C16C2
socleC2×C3×C7D8
hypercenterC7×C16D3
hypocenterC3C7×D16
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C7 ◁ C4×C7 ◁ C7×C8 ◁ C7×C16

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 336

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26);(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)(25,26)

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13050846, #13050848, #13050850, …
maximal normal subgroup of#13050846, #13050848, #13050850, …
maximal quotient ofC7×#4449, C7×D96, C7×Dic48, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 179);